You have a mass of 55kg and are riding your frictionless skateboard, which has a mass of 5kg, in a straight line at a speed of 4.5 m/s when a friend standing on a balcony above you drops a 2.5 kg sack of flour straight down into your arms. What is your new speed, while holding the flour sack

Given

m1 (mass of the first object) : 55 Kg

m2 (mass of the second object) : 55 Kg

v1 (velocity of the first object) : 4.5 m/s

v2 (velocity of the second object) : ?

m3 (mass of the object dropped) : 2.5 Kg

The law of conservation of momentum states that when two bodies collide with each other, the momentum of the two bodies before the collision is equal to the momentum after the collision. This can be mathemetaically represented as below:

Pa = Pb

Where Pa is the momentum before collision and Pb is the momentum after collision.

Now applying this law for the above problem we get

Momentum before collision = momentum after collision.

Momentum before collision = (m1+m2) x v1 = (55+5) x 4.5 = 270 Kgm/s

Momentum after collision = (m1+m2+m3) x v2 = (55+5+2.5) x v2

Now we know that Momentum before collision = momentum after collision.

Hence we get

270 = 62.5 v2

v2 = 4.32 m/s